Your example is from 2.4(b)(1) of the style manual for "Commission and Agency Documents and Materials".
The New York Public Employment Relations Board is a state level version of the National Labor Relations Board (NLRB) that governs private sector management-union relations nationwide, for public employees in New York State. These boards have both regulatory power like any other government agency, and the quasi-judicial authority to resolve union-management disputes outside of the regular court system.
The cited document is an opinion of the New York Public Employment Relations Board decided in 1998 and reported in the case reporter "Public Employment Relations Board Reports" in volume 31 as decision number 4021 in that volume, for which the paragraph symbol (¶) is used in their official form of citation (the section symbol is §). The decisions are available on the Internet (without the citations from the case reporter) at http://www.perb.ny.gov/nys-perb-board-decisions/
The use of the ¶ is a bit quirky, but has a logic to it. If no section or paragraph mark were used, the reference would be to a page number in that volume of the case reporter under default rules for interpreting citations. But, since this is a reference to a sequential entry in the case reporter, rather than to a page number, some symbol must be used to identify it. The use of the ¶ symbol to break up logical components of a volume parallels the practice for learned legal treatises and legal services which usually break up their logical units by components denoted with the paragraph mark.
The case name "(Matter of Freeport Union Free Sch. Dist. [Freeport Educ. Off. Assn.]" means that the case was in regard to employees of the Freeport Union Free School District, and the bracketed portion means that the other party in the dispute was the Freeport Education Officials Association (i.e. the teacher's union).